Original Articles

On the Maximal Function for the Generalized Ornstein-uhlenbeck Semigroup.

Published in: Quaestiones Mathematicae
Volume 30 , issue 4 , 2007 , pages: 471–482

DOI: 10.2989/16073600709486214

Author(s): Jorge Betancor , Liliana Forzani , Roberto Scotto , WilfredoO. Urbina

Keywords: GENERALIZED HERMITE ORTHOGONAL POLYNOMIALS , MAXIMAL FUNCTIONS , GAUSSIAN MEASURE , NONDOUBLING MEASURES

Abstract

In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in R associated with the generalized Hermite polynomials {H ^μ _n} and prove that it is weak type (1,1) with respect to dλ_μ(x) = |x|^2μ e ^−|x|² dx, for μ > –1/2 as well as bounded on L^p (dλ_μ) for p > 1.

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